document.write( "Question 1141483: Four years ago a man was 2 and a 1/2 times as old as his son, but in five years time, he will only be twice as old as his son. How old is the man now? \n" ); document.write( "

Algebra.Com's Answer #762050 by ikleyn(52776) $\"\"$ $\"About$

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document.write( "Let y be the man's age, and\r\n" );
document.write( "let n be the son's age.\r\n" );
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document.write( "From the condition, you have these two equations\r\n" );
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document.write( "y-4 = ,             (1)\r\n" );
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document.write( "y+5 = 2(n+5).               (2)\r\n" );
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document.write( "Simplify, by multiplying equation (1) by 2 (both sides)'\r\n" );
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document.write( "2y-8 = 5n-20,               (1')\r\n" );
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document.write( "y+5 = 2n+10                 (2')\r\n" );
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document.write( "2y-5n = -12,                (3)\r\n" );
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document.write( "y-2n = 5.                   (4)\r\n" );
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document.write( "Multiply equation (3) by 2;\r\n" );
document.write( "Multiply equation (4) by 5.\r\n" );
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document.write( "4y-10n = -24,               (5)\r\n" );
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document.write( "5y-10n =  25                (6)\r\n" );
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document.write( "Subtract equation (5) from equation (6). You will get\r\n" );
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document.write( "5y - 4y = 25 - (-24)\r\n" );
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document.write( "y       = 49\r\n" );
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document.write( "ANSWER.  The man's age is 49 years.\r\n" );
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document.write( "CHECK.   Then from equation(2),  49+5 = 2*(n+5)  ====>  54 = 2*(n+5)  ====>  n+5 = 54/2 = 27  ====>  n = 27-5 = 22.\r\n" );
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document.write( "         Thus the son's age is 22 years, and you can check that the equation (1) is valid, too.  The check is completed.\r\n" );
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